Answer:
The correct answer is "100".
Explanation:
The given values are:
X (mean) = 5
X (standard deviation) = 25
Variance of X will be:
= [tex]25^{2}[/tex]
= [tex]625[/tex]
The solution of the part first is:
The given equation is :
[tex]Y=2+4X[/tex]
On putting the value of x in above equation we get ,
[tex]Y=2+4\times 5 \\Y=2+20\\Y=22[/tex]
So we get the mean of Y is 22
For finding the S.D of Y
[tex]Y = 2+4X\\[/tex]
So,
variance of Y= Var(2+4X)
As we know that the variance of constant is zero
So, variance (2) =0
⇒ [tex]Variance(aX) = a^2Variance(X)[/tex]
⇒ [tex]Var(4X) = 42Var(X) = 16Var(X)[/tex]
So,
⇒ [tex]Variance(Y) = Variance (2) + Variance(4X)[/tex]
We know the variance of constant is zero
So, var(2)=0
⇒ [tex]Variance(Y)= 16\times 625\\ Variance(Y)=10000[/tex]
Thus the standard deviation of Y is:
= [tex](10000)^{0.5}[/tex]
= [tex]100[/tex]
